# Visualizing Physical Units in Phyiscs

I do best in physics when I can make sense of the units that accompany values, and I do this by visualizing in my mind what is happening. Take for instance, $v=\frac{s}{t}$. When I think of velocity I can visually see an object moving a distance, $s$, over a certain time, $t$. What I struggle with though are units that aren't 'x per y'. Like meters per second.

Take impulse: $N\cdot s$ or Newtons: $\frac{kg \cdot m}{s^2}$. How can I visualize a Newton-second or a Kilogram-meter.

If you look at a product or division, the way is to start with one thing.

Look at 'Newton-second'. This means a newton applied for a second. A newton is a force, a shove, so to speak. You shove something for a second, and it starts moving. If it weighs a kilogram, the effect of a newton-second is to make it move at 1 m/s. If it weighs 10 kg, it will move at 1 dm/s.

A metre-newton of torque, is where you pull on a handle with newtons of force, at a distance of metres. The old rusty nut isn't going to turn too fast unless you get a longer spanner. Then you need to pull more to get the same angle, but it's a bigger force.

If you get something like 'volts per metre', it's a gradient. 'per metre' often gives gradients, or weights of wire. So volts per metre here is a gradient. The unit translates to newtons per coulomb, and it's the electric force doing the shoving. Here the size of the handle is in coulombs, and the newtons come as force.

Sometimes it's better to look at how the quantity is defined, and then see if you can make the units to work. One quantity I came across was 's/m' of permeability. It works like this. The actual thing is 'flow of liquid per area, divided by the driving pressure', so (kg / m² s) / Pa. But when you put Pa = kg / m s², the division gives s/m.

Another unit is 'W/m K'. This is thermal conductivity, or energy flux per driving temperature gradient. What it means is (energy / area / time ) ÷ (temperature / thickness). The fps unit is Btu / ft² h ÷ °F / in, or the unit Btu in / ft² hr °F. Replacing these with their metrics, gives J⋅m/m² s K, or W/m K.

• Beautiful answer Commented Oct 3, 2019 at 18:57
• I think this was the answer the OP was looking for. "$x$ per $y$" is easy to understand; "$x\times y$" is more difficult, but "$x$ applied $y$ times" is a great intuitive way to understand it.
– pela
Commented Oct 3, 2019 at 18:58

Physical units essentially keep track of the measurement processes needed to determine the quantities you are dealing with. Once you understand the procedure to derive those quantities, the actual units are irrelevant, especially because changing the measurement apparati may result in different definitions of the units themselves. The standard example is that of special relativity: if you fix the velocity of the signals you are dealing with (say, $c$) then measurements of times can be addressed to measurement of distances, and viceversa; therefore the two quantities may end up being defined with the same units.

This said, the attitude of trying to visualise things is unfortunate: not everything can be visualised (but can be understood, on the other hand). I do not see the difference, in your example, between visualising the velocity and the impulse: they are equally hard to imagine unless you know how to perform an underlying experiment to determine them. But if you did have an experiment to calculate the impulse then it would be straightforward to understand what it is.

• I understand your point, what I am trying to accomplish though is that when I see a value of say $J=20 \space N\cdot s$ and someone asked me what that is as if telling to a child. I can't say that, that is the value of the change in momentum during a time, $t$. For someone who doesn't know what momentum, impulse actually is this would be like talking latin. Like $v=\frac{x}{t}$ I can say that the velocity is the distance something goes in a certain time period. 3$\frac{m}{s}$ travels 3 meteres in 1 one second. That is easily understandable, but what about Impulse or other similiar units? Commented Dec 2, 2015 at 17:38
• I don't see how the notions of velocity, distance and time are easier to understand than the rest; if you don't know what time is, velocity can be equally hard to picture. The take home message is that it only makes sense to talk about things if you know what the underlying quantities and principles are (if someone doesn't know what force is, what's the point of explaining what the impulse is, on top?). Commented Dec 2, 2015 at 17:52

I find that newtons are easiest to intuitively understand if I think of it as corresponding to how much force I have to put on an object to keep it from falling. The heavier the object, the more force I need, but in a different gravitational environment, I would not have to use as much force, even though the mass of the object would not have changed.